فهرست نشریات علمی دسترسی آزاد ایران

‎Let $G=(V,E)$ be a graph‎. ‎The entire Sombor index of graph ‎$‎G‎$‎, $ SO^\varepsilon(G) $ is defined as the sum of the terms‎‎$\sqrt{d_{G}^2(a)+d_{G}^2(b)}$‎, ‎where $a$ is either adjacent to or incident with $b$ and‎‎$a,b\in V\cup E$‎.‎It is known that if $T$ is a tree of order $n$‎, ‎then $SO^\varepsilon(T)\ge 6\sqrt{5}+8(n-3)\sqrt{2}$‎. ‎We improve this result and establish best lower bounds on the entire Sombor index with given vertices number and maximum degree‎. ‎Also‎, ‎we determine the extremal trees achieve these bounds.